Question

Atmost how many digits are there in the square of a number of three digits​

Answer 1

In the last article on tips and tricks, we saw how to calculate the cube root in less than 5 seconds. Today, we are going to have a look on a simple method that can help you to calculate the square of 3 digit number quickly. Though the method may look confusing & difficult initially, once you get the hang of the formula, you will find it much easier.

square of 3 digit number

Calculating the square of 3 digit number quickly

Let us have a look at the method first.  

Let the three digit number whose square is to be calculated be XYZ. Sq (XYZ) is calculated in following manner.

STEP 1.         Last digit = last digit of SQ (Z)

STEP 2.        Second Last Digit = 2*Y*Z +  carryover from STEP 1.

STEP 3.        Third Last Digit 2*X*Z+ Sq (Y) +  carryover from STEP 2.

STEP 4.        Fourth last digit is 2*X*Y +  carryover from STEP 3.

STEP 5.        In the beginning of the result (the first digit) will be Sq (X) + any carryover from Step 4.

For those who got confused with the above formula, we have some examples shown below:

Examples to calculate square of 3 digit numbers quickly

What is the Square of 421

STEP 1.           Last digit = last digit of SQ (1) =1

STEP 2.          Second Last Digit = 2*2*1 + any carryover from STEP 1= 4

STEP 3.          Third Last Digit 2*4*1+ Square (2) + any carryover from STEP 2=8+4=12

As, a result 2 would be the third last digit and 1 is the carryover.

STEP 4.          Fourth last digit is 2*4*2 + any carryover (which is 1) = 16+1=17.

So, 7 is the digit and carry over 1.

STEP 5.         In the beginning  result will be Sq (4) + any carryover from Step 4.

So 16+1 =17.

So the final result will be  177241.

2) What is the square of 511?

STEP 1.        Last digit = last digit of SQ (1) =1

STEP 2.       Second Last Digit = 2*1*1 + any carryover from STEP 1= 2

STEP 3.       Third Last Digit 2*5*1+ Square (1) + any carryover from STEP 2 which is   10+1=11.

So, 1 would be the third last digit  and 1 carryover.

STEP 4.        Fourth last digit is 2*5*1 + any carryover (which is 1) = 10+1=11.

So, 1 and carry over 1.

STEP 5.        In the beginning of the result will be Sq (5) + any carryover from Step 4.

So, we get   25+1=26.

Therefore , the square of the number 511 would be 261121.

Hope, you enjoyed learning the concept.

Practice the formula with a few more examples. If you practice it often, you would easily be able to calculate the square of 3 Digit Numbers in less than 10 seconds.

Now, try calculating the square of 647 and SHARE HERE the time you took to calculate its square.

All the Best

Answer 2

Step-by-step explanation:

Let us consider 1st number as 1

No. of digit : 1

Square : 1

2

=1

No. of digit in square = 1

satisfying options (B) and (C)

Now let us consider 2nd number as 4

No. of digit : 1

Square : 4

2

=16

No. of digit in square = 2

satisfying options (D)

If we take 3rd number as 25

No. of digit : 2

Square : 25

2

=625

No. of digit in square = 3

satisfying options (B)

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